Solving for x in k=(x)ln(x): A Daunting Task

  • Thread starter Ja4Coltrane
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In summary, the equation k=(x)ln(x) does not have a solution that can be written as an explicit formula "x = something". It can be solved numerically for any given value of k. This is because many seemingly simple equations, including this one, do not have explicit solutions and can only be solved numerically. The fact that equations in exercises typically have solutions may lead to the misconception that all equations can be solved explicitly.
  • #1
Ja4Coltrane
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I was wondering how one would solve for x in the equation
k=(x)ln(x)

I tried all normal means. For example rewriting the equation with the x as an exponent of x. I have tried writing it in exponential form and the raising both sides to the power -k. I basically have no idea how to do this.
I do notice that the x sort of functions in the way that it would in a damping function...does that have anything to do with it?
 
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  • #2
Many "simple looking" equations, including your equation, do not have solutions that can be written as an explicit formula "x = something".

It is easy to solve the equation numerically, for any given value of k.

Of course the equations that occur in exercises all DO have solutions, and that might mislead you into thinking that any equation can be solved explicitly.
 

FAQ: Solving for x in k=(x)ln(x): A Daunting Task

What is the purpose of solving for x in k=(x)ln(x)?

The purpose of solving for x in k=(x)ln(x) is to find the value or values of x that satisfy the given equation. This is important in many fields of science, such as physics, chemistry, and engineering, where equations are used to model and understand real-world phenomena.

Why is solving for x in k=(x)ln(x) considered a daunting task?

Solving for x in k=(x)ln(x) can be considered daunting because it involves a logarithmic function, which can be complex to manipulate algebraically. Additionally, there may be multiple solutions or no real solutions at all, making the process more challenging.

What strategies can be used to solve for x in k=(x)ln(x)?

Some strategies that can be used to solve for x in k=(x)ln(x) include graphing, substitution, and using the Lambert W function. Additionally, numerical methods such as Newton's method can be used to approximate the solutions.

What are some common mistakes when solving for x in k=(x)ln(x)?

Some common mistakes when solving for x in k=(x)ln(x) include not considering the domain of the logarithmic function, forgetting to check for extraneous solutions, and incorrectly applying logarithmic rules. It is important to carefully follow the steps and check the solutions to avoid these mistakes.

How is solving for x in k=(x)ln(x) relevant to real-world applications?

Solving for x in k=(x)ln(x) is relevant to real-world applications because it allows us to understand and make predictions about natural phenomena. For example, in biology, the growth of populations can be modeled using logarithmic functions, and solving for x can help determine the carrying capacity of a species in a particular environment.

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